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Grade 12 Mathematics (Social Science) national exam, 2013 E.C. (2021 G.C.)

22 questions · 180 minutes. The first 5 answers are shown with explanations; sit the whole paper timed in the app to get your score and the textbook page behind every question.

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  1. 1.On the average, which of the following is less significant as a factor to save money in a saving institution in our context?
    • A. Save for charity and donations
    • B. Save for emergency needs
    • C. Save for retirement
    • D. Save for medical cases
  2. 2.Store-I sells a dozen of pens for 54 Birr and Store-II sells 5 pens of the same brand for 23 Birr. If a clerk wants to buy 100 pens from economical sales, then how much can he save in Birr?
    • A. 12.50
    • B. 10.00
    • C. 8.50
    • D. 9.00
    Answer: B. The key idea is to compare the price per pen. Store-I charges $54\div12=4.50$ Birr per pen, while Store-II charges $23\div5=4.60$ Birr per pen; for $100$ pens, the saving is $100(4.60-4.50)=10$ Birr, so B. A, C, and D are not the difference in cost. Textbook: Grade 12, unit 4 · section 4.2.
  3. 4.Which of the following is an advantage of using the techniques of random sampling in statistical methods?
    • A. Each techniques of sampling is applicable to any type of population
    • B. A person with limited know-how can apply the techniques
    • C. The investigator personally cannot be a source of bias
    • D. The sample collected may not be a good representative
    Answer: C. Random sampling helps prevent the investigator from choosing a sample in a biased way. Thus C describes an advantage of random sampling. A is wrong because not every sampling technique suits every population. B is wrong because sampling methods may require knowledge and care. D describes a possible weakness, not an advantage. Textbook: Grade 12, unit 3 · section 3.4.
  4. 5.The amount of sales in a business enterprise is directly proportional to the number of items sold and inversely to the amount of tax paid, which is 5% of the total amount sold. If the sales amount to 15000 Birr and the number of items sold is 3000, what is the constant of proportionality in this situation?
    • A. 5700
    • B. 7500
    • C. 3650
    • D. 3750
  5. 6.In leasing a building, tax is required from rental income. The following is the tax rate on a total amount of rent per year in Birr. Amount taxable income Up to 1,800 1,801 – 7,800 7,801 – 16,800 16,801 – 28,200 Tax rate 0% 10% 15% 20% Deducted amount 0 180 570 1,410 If a shop is rented at 2,350 Birr per month for one year, what amount of tax is payable in Birr?
    • A. 3,750
    • B. 2,420
    • C. 5,460
    • D. 4,230
  6. 8.Which one of the following defines a one-to-one function?
    • A. $f ={(x, y): x \text{ is a sister of } y}$
    • B. $f ={(x, y): y = 3x - 1}$
    • C. $f ={(x, y): y = x^{2} + 1}$
    • D. $f = {(x, y): y \text{ is a father of } x}$
  7. 14.What are the modulus and argument of the complex number $2 + 2i$ respectively?
    • A. $\sqrt{2}$ and $\pi/4$
    • B. $2$ and $\pi/4$
    • C. $2\sqrt{2}$ and $-\pi/4$
    • D. $4$ and $\pi/4$
A Cottage industry produces goods either by capital or labour intensive method according to: i) capital intensive using 1 unit of labour and 4 units of capital. ii) labour intensive using 5 units of labour and 2 units of capital. The industry manages to arrange up to 200 units of labour and 130 units of capital.
  1. 22.If the owner can sell goods at a constant price and get a profit of 100 Birr per unit of the two quantities of goods produced by the processes i) and ii), what will be the maximum profit generated?
    • A. 4,000 Birr
    • B. 4,500 Birr
    • C. 5,000 Birr
    • D. 5,500 Birr
  2. 24.The following table shows the mean and standard deviation of expenditures in Birr of three factories F1, F2, and F3, in a week. F1 F2 F3 Mean 12,500 12,500 2,500 Standard deviation 3.62 3.56 3.6 Which factory or factories show more consistency in their expenditures than the other(s)?
    • A. Factories F1 and F3
    • B. Factories F1 and F2
    • C. Factory 1
    • D. Factory 2
    Answer: D. Consistency means that the values vary less compared with their mean, so compare standard deviation divided by mean. For $F_1$ and $F_2$, the means are equal, and $3.56<3.62$; $F_3$ has a much smaller mean with a similar standard deviation. A is wrong because $F_3$ is less consistent. B is wrong because $F_1$ has more variation than $F_2$. C is wrong because $F_2$ is more consistent than $F_1$. Textbook: Grade 9, unit 9 · section 9.2.
  3. 25.Consider the data given below: 10, 12, 10, 15, -12, 16, 13, 11, 12, 15 The mean deviation about the mode of this data is equal to
    • A. 1.8
    • B. 2.0
    • C. 1.5
    • D. 1.6
  4. 26.On the graph of the cumulative frequency distribution of a certain data, it is observed that, the mean, median, mode and standard deviation are 9.8, 10.0, and 2.1, respectively. Which of the following is a correct conclusion about this distribution?
    • A. Most of the data values lie to the right of the modal value.
    • B. Most of the data values lie to the left of the modal value.
    • C. The data values are symmetrically distributed.
    • D. The distribution is skewed to the positive.
  5. 27.Which of the following is a geometric sequence?
    • A. 1, 1.5, 2.5, 3.5, ...
    • B. 0.1, 0.01, 0.0011, 0.000111, ...
    • C. 8, -4, 2, ...
    • D. 0.1, 0.11, 0.12, 0.13, ...
    Answer: C. A geometric sequence has the same ratio between each pair of consecutive terms. In C, $-4\div 8=2\div(-4)=-\frac{1}{2}$, so the ratio is constant. A has changing ratios. B has changing ratios. D has a constant difference, not a constant ratio. Textbook: Grade 12, unit 1 · section 1.2.
  6. 28.A factory that produces electric cable had sales Birr 1,000,000 the first day. During each successive day the sales increased by Birr 10,000 every day. What is the total sales of the factory in the first 10 days?
    • A. Birr 10,000,000
    • B. Birr 1,000,000
    • C. Birr 20,900,000
    • D. Birr 10,450,000
  7. 31.Which one of the following sequences is a null sequence?
    • A. $\left\{n\sin\left(\frac{1}{n}\right)\right\}$
    • B. $\left\{1-\frac{1}{n}\right\}$
    • C. $\left\{\frac{n}{n+1}\right\}$
    • D. $\left\{\frac{\cos n}{n}\right\}$
    Answer: D. A null sequence is a sequence whose terms approach $0$. For D, $\left|\frac{\cos n}{n}\right|\leq\frac{1}{n}$, and $\frac{1}{n}$ approaches $0$. A approaches $1$; B approaches $1$; C approaches $1$. Textbook: Grade 11, unit 6 · section 6.4.
  8. 32.Suppose ${a_n}$ and ${b_n}$ are sequences with $\lim_{n\to\infty} a_n = L$ and $\lim_{n\to\infty} b_n = M$. Then which of the following is NOT necessarily true?
    • A. $$\lim_{n\to\infty}(3a_n + 2b_n) = 3L + 2M$$
    • B. $$\lim_{n\to\infty}(a_n - b_n) = L - M$$
    • C. $$\lim_{n\to\infty}(a_nb_n) = LM$$
    • D. $$\lim_{n\to\infty}\left(\frac{a_n}{b_n}\right) = \frac{L}{M}$$
    Answer, explanation and textbook page: open in the app.
  9. 36.What are the 2$^{\text{nd}}$ and the 3$^{\text{rd}}$ derivative of $f(x) = e^x$ respectively?
    • A. $4f(x)$ and $2^{n}f(x)$
    • B. $2f(x)$ and $nf(x)$
    • C. $9f(x)$ and $3^{n}f(x)$
    • D. $9f(x)$ and $n^{2}f(x)$
    Answer, explanation and textbook page: open in the app.
  10. 38.What are the length $L$ and width $W$ of a rectangle with perimeter 10,000m that maximizes the area?
    • A. $L = 2,500 \text{ m and } W = 3,000 \text{ m}$
    • B. $L = 2,500 \text{ m and } W = 2,500 \text{ m}$
    • C. $L = 5,000 \text{ m and } W = 5,000 \text{ m.}$
    • D. $L = 5,000 \text{ m and } W = 2,500 \text{ m.}$
    Answer, explanation and textbook page: open in the app.
  11. 39.If the radius $r$ of a sphere is increasing at the rate of 2 cm/min, then the rate of change of the volume when $r = 1 \text{ cm}$ is
    • A. $6\pi \text{ cm}^3/\text{min}$
    • B. $4\pi \text{ cm}^3/\text{min}$
    • C. $12\pi \text{ cm}^3/\text{min}$
    • D. $8\pi \text{ cm}^3/\text{min}$
    Answer, explanation and textbook page: open in the app.
  12. 42.Which of the following is equal to $\int (\cos x - 2x)\, \mathrm{d}x$ where $c$ is a constant?
    • A. $\sin x + x^2 + c$
    • B. $-\sin x - x^2 + c$
    • C. $\sin x - x^2 + c$
    • D. $-\sin x + x^2 + c$
    Answer, explanation and textbook page: open in the app.
  13. 43.What is the area of the region bounded by $y = 0$ and the graph of $f(x) = 4 - x^2$ on the interval $[-1, 1]$?
    • A. $\frac{22}{3}$
    • B. $\frac{2}{3}$
    • C. $\frac{26}{8}$
    • D. $2$
    Answer, explanation and textbook page: open in the app.
  14. 45.A shop sales a pack of 20 articles for 5,500 Birt. It planned to clear the articles during a holiday. If the shop sells each item for 220 Birt, what percent discount has it made?
    • A. 20%
    • B. 22%
    • C. 15%
    • D. 18%
    Answer, explanation and textbook page: open in the app.
  15. 53.Which of the following is true where $c$ is a constant?
    • A. $\int \frac{\sin\sqrt{x}}{\sqrt{x}} \,\mathrm{d}x = -2\cos\sqrt{x} + c$
    • B. $\int (3x + 5)^5\,\mathrm{d}x = \frac{(3x + 5)^7}{7} + c$
    • C. $\int \ln\,\mathrm{d}x = \frac{1}{x} + c$
    • D. $\int xe^{\,x}\,\mathrm{d}x = \frac{x^2}{2} + c$
    Answer, explanation and textbook page: open in the app.
Other Mathematics (Social Science) years: 2018 2017 2016 2015 2014